Course Details in 2020/21 Session

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Module Title LM Game Theory and Multicriteria Decision Making Mathematics Mathematics 06 33867 Dr Sergey Sergeev Masters Level 20 Semester 2 LI Linear Algebra & Linear Programming - (06 25765) None Lecture-46 hours Tutorial-10 hours Guided independent study-144 hours Total: 200 hours The first half of this module presents game theory as the study of decision-making in competitive situations. It provides an introduction to the theory of finite and infinite games with a particular emphasis on 2-person games. All results will be presented in a rigorous way and accompanied, wherever possible, by showing economic applications. This module also demonstrates that the results and concepts of other branches of mathematics (like the fixed point theorem, convexity, duality) have practical interpretation and use. The second half of this module explores multicriteria or multiobjective optimisation where several conflicting objectives have to be optimised simultaneously: stock portfolios have to be chosen such that the portfolio maximises the return and simultaneously minimises the risk; health care has to be managed such that the service is efficient yet not too costly; hazardous material has to be transported such that risk as well as costs incurred are minimal; bridges and buildings have to be designed such that they can be built cheap but still with maximum stability etc. As such, multicriteria problems are of prime importance for decision makers in the private as well as the public sector. This module brings together various ideas from geometry and analysis in studying solutions and solution methods for multicriteria problems in management and science. By the end of the module students should be able to: Understand and use the main concepts of game theory like optimal strategies, stable sets and the core of the game Formulate games from economic narratives Use a range of methods for solving these games Explore the topic beyond the taught syllabus Understand and explain the basic concepts of multicriteria optimisation Formulate real-world problems from management and science as multicriteria optimisation problems Discuss different solution concepts 33867-01 : Raw Module Mark : Coursework (100%) Assessment: 2 hour Summer Examination (50%); In-course Assessment (50%).